The cue sports include pool, billiards, and snooker, and have recently enjoyed a surge in popularity worldwide. There have been a number of efforts at developing automation aids for these games. One example is the Instant Pool Trainer [Lar01], in which a camera is mounted on the ceiling aimed down at the table. Acquired images are transmitted to a computer and automatically analysed using image processing techniques. The system makes suggestions to the human trainee about the next shot to place, the desired angle of the cue, etc.
Other systems have attempted to fully automate the play by adding a robotic component [Nak01, Qi99, Shu94, Chu02, Ali04, Lon04, Che04]. In addition to the ceiling-mounted camera, these systems involve some form of computer-controlled robotic actuation device that can position a cue to the correct location and place a shot. The most common example of such robotic devices are gantry systems [Ali04, Lon04, Che04, Shu94], the first of which was proposed by Shu et al. [Shu94]. Other proposed robotic devices include a mobile robot that moves around the perimeter of the table and extends a cue-like end-effector to place a shot [Qi99], and a mobile robot that moves over the surface of the table [Lar02].
The cue sports demand a high degree of positional accuracy when placing a shot, and one of the main challenges of a robotic system is to position the cue to the desired location with sufficient accuracy. The exact positional accuracy that is required to play well has not been reported in the literature, and is presumed to be unknown, although it is likely to be on the order of 0.1 mm or finer. Whereas mechanical devices can be positioned very precisely, both sensor errors and robot calibration contribute to limitations to positioning accuracy of such systems.
In the above cases where overhead cameras are the primary sensor to resolve position, a limitation to accuracy is sensor resolution. Standard CCD cameras that are suitable for machine vision applications will often have 640×480 pixels. If the entire length of a standard pool table extends the complete 640 pixels, then this resolves to ˜4 mm/pixel, which is at least an order of magnitude too coarse. Using higher pixel-count sensors, or multiple cameras, are possible remedies. In the case of multiple sensors, each of which images a smaller region of the table at a higher magnification, combining the partial images acquired by each individual sensor into a global coordinate frame requires accurate calibration of the extrinsic camera parameters. Radial distortions in the optical systems also limit the accuracy of the cameras. A further limitation is that, from the overhead vantage, the table appears as a 2-D plane, and vertical displacements of the cue (i.e., normal to the camera place) cannot be perceived. Controlling these vertical displacement to allow the system to strike the cue ball high or low forms an important part of the play.
The main limitation to positional accuracy is calibration of the robotic device [Lon04]. The proper calibration of robotic devices to ensure positional accuracy is a well-known and challenging problem. The majority of robotic devices are equipped with joint encoders that very precisely measure the location of each revolute or translational joint. Despite their precision, converting these joint values into an accurate position of the robotic end-effector is not straightforward, as there are a number of factors that cannot be directly measured which affect the overall accuracy. The majority of industrial robotic devices do not require absolute positioning accuracy, so long as they are precise and repeatable, so this limitation on accuracy does not present a barrier to use in many cases. An exception where absolute positioning accuracy is required are Coordinate Measurement Machines (CMMs). These devices are finely machined and calibrated so that they can be used in metrological inspection applications. The delicate mechanisms used in CMM construction would unfortunately not be able to withstand a significant load or impact, such as striking a ball.
In human play, it is an accepted practice to accurately align the cue prior to a shot by locating the eye closely to the axis of the cue [Kan99]. From this vantage, the locations of both the cue ball (which is to be impacted by the cue) and the object ball (which is to be impacted by the cue ball) can be seen. Small positional variations of the cue axis as well as of the tip of the cue can be perceived accurately, as they are parallel to the human's retinal plane. Conversely, motions that are perpendicular to the retinal plane, such as those parallel to the cue axis, are less easily resolved, and are fortunately less important to accurate shot placement.
Therefore, there is a need to provide a robotically controlled pool game which overcomes the aforementioned shortcomings.